Do You Want To Do That With CSS? — Align Elements Left and Right

There are various "tasks" designers wish to have happen in the display of their pages, using CSS, that seem like they ought to be simple to do. The need for accomplishing the tasks is common to most web authors sooner or later, but the techniques used to do them are not widely known in the community yet.
Our first "task" involves placing two items in a box, and having them display on opposite sides of that box. Let's look at ways we can align elements left and right using CSS.